Related papers: Threshold scattering for the focusing NLS with a r…
In this paper, we consider the scattering theory of the radial solution to focusing energy-subcritical Hartree equation with inverse-square potential in the energy space $H^{1}(\mathbb{R}^d)$ using the method from \cite{Dodson2016}. The…
This paper is concerned with the global well-posedness and finite time blowup problem for the 3D focusing energy-critical inhomogeneous NLS. In the previous results \cite{chkl2, chkl3} the authors considered the same problems with the…
In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator consisting of regular and singular parts. In this paper, the…
In this paper, we prove scattering asymptotics for the 2D (discrete dimension) cubic resonant system. This scattering result was used in Zhao \cite{Z1} as an assumption to obtain the scattering for cubic NLS on $\mathbb{R}^2\times…
We consider the 3-dimensional nonlinear Schr\"{o}dinger equation (NLS) with average nonlinearity. This is a limiting model of NLS with strong magnetic confinement and a generalized model of the resonant system of NLS with a partial harmonic…
We consider the fixed angle inverse scattering problem and show that a compactly supported potential is uniquely determined by its scattering amplitude for two opposite fixed angles. We also show that almost symmetric or horizontally…
We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and Weder in 1995, we prove that the high-velocity limit of the…
We consider the Schr\"odinger equation with a multipoint potential of the Bethe-Peierls-Thomas-Fermi type. We show that such a potential in dimension d=2 or d=3 is uniquely determined by its scattering amplitude at a fixed positive energy.…
In this paper, we show the scattering and blow-up result of the radial solution with the energy below the threshold for the nonlinear Schr\"{o}dinger equation (NLS) with the combined terms iu_t + \Delta u = -|u|^4u + |u|^2u \tag{CNLS} in…
We prove global well-posedness and scattering for the defocusing, cubic NLS on $\mathbb{R}^3$ with initial data in $H^s(\mathbb{R}^3)$ for $s>49/74$. The proof combines the ideas of resonance decomposition in \cite{CKSTT4} and…
A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…
The inverse scattering transform for the focusing nonlinear Schrodinger equation is presented for a general class of initial conditions whose asymptotic behavior at infinity consists of counterpropagating waves. The formulation takes into…
In this review paper we carry on our investigations on Schroedinger operators with inverse square potentials on the half-line. Depending on several parameters, such operators possess either a finite number of complex eigenvalues, or an…
We prove scattering for small solutions to of nonlinear Schroedinger equations in 1D with a space periodic potential
We prove sharp $L^\infty$ decay and modified scattering for a one-dimensional dispersion-managed cubic nonlinear Schr\"odinger equation with small initial data chosen from a weighted Sobolev space. Specifically, we work with an averaged…
The study of obstacle scattering for the Klein-Gordon equation in the presence of long-range magnetic potentials is addressed. Previous results of the authors are extended to the long-range case and the results the authors previously proved…
Potentials are constructed for the lambda-nucleon interaction in the $^1\text{S}_0$ and $^3\text{S}_1$ channels. These potentials are recovered from scattering phases below the inelastic threshold through Gel'fand-Levitan-Marchenko theory.…
We consider the inverse random potential scattering problem for the two- and three-dimensional biharmonic wave equation in lossy media. The potential is assumed to be a microlocally isotropic Gaussian rough field. The main contributions of…
This work explores the global existence and scattering behavior of solutions to a damped, inhomogeneous nonlinear Schrodinger equation featuring a time-dependent damping term, an inverse-square potential, and an inhomogeneous nonlinearity.…
We are concerned with the acoustic scattering problem by many small rigid obstacles of arbitrary shapes. We give a sufficient condition on the number $M$ and the diameter $a$ of the obstacles as well as the minimum distance $d$ between them…